Properties that are common to all distributions are accessed via non-member
getter functions. This allows more of these functions to be added over
time as the need arises. Unfortunately the literature uses many different
and confusing names to refer to a rather small number of actual concepts;
refer to the concept index to find
the property you want by the name you are most familiar with. Or use the
function index to go straight to
the function you want if you already know its name.

For a continuous function, the probability density function (pdf) returns
the probability that the variate has the value x. Since for continuous
distributions the probability at a single point is actually zero, the probability
is better expressed as the integral of the pdf between two points: see
the Cumulative Distribution Function.

For a discrete distribution, the pdf is the probability that the variate
takes the value x.

This function may return a domain_error
if the random variable is outside the defined range for the distribution.

For example for a standard normal distribution the pdf looks like this:

Returns the supported range of random variable over the distribution dist.

The distribution is said to be 'supported' over a range that is "the smallest
closed set whose complement has probability zero". Non-mathematicians
might say it means the 'interesting' smallest range of random variate x
that has the cdf going from zero to unity. Outside are uninteresting zones
where the pdf is zero, and the cdf zero or unity.

Where μi is the i'th central moment of the distribution, and in particular
μ2 is the variance of the distribution.

The kurtosis is a measure of the "peakedness" of a distribution.

Note that the literature definition of kurtosis is confusing. The definition
used here is that used by for example Wolfram
MathWorld (that includes a table of formulae for kurtosis excess
for various distributions) but NOT the definition of kurtosis
used by Wikipedia which treats "kurtosis" and "kurtosis
excess" as the same quantity.

kurtosis_excess='proper'kurtosis-3

This subtraction of 3 is convenient so that the kurtosis excess
of a normal distribution is zero.

This function may return a domain_error
if the distribution does not have a defined kurtosis.